Devices with fluidic nanofunnels, associated methods, fabrication and analysis systems

ABSTRACT

Methods of forming a chip with fluidic channels include forming (e.g., milling) at least one nanofunnel with a wide end and a narrow end into a planar substrate, the nanofunnel having a length, with width and depth dimensions that both vary over its length and forming (e.g., milling) at least one nanochannel into the planar substrate at an interface adjacent the narrow end of the nanofunnel.

RELATED APPLICATIONS

This application is a 35 USC § 371 national phase application ofPCT/US2013/025078, with an international filing date of Feb. 7, 2013,which claims the benefit of and priority to U.S. Provisional ApplicationSer. No. 61/597,364, filed Feb. 10, 2012, the content of which is herebyincorporated by reference as if recited in its entirety herein.

STATEMENT OF FEDERAL SUPPORT

This invention was made with government support under Grant No.R01-HG002647 awarded by the National Institutes of Health. The UnitedStates government has certain rights in the invention.

FIELD OF THE INVENTION

This invention relates to fluidics and microelectronic devices.

BACKGROUND OF THE INVENTION

There has been considerable recent interest in the incorporation ofnanoscale components in lab-on-a-chip fluidic devices. This interestowes its origin to several advantages (and differences that may beadvantageously leveraged) in moving from the micron scale to thenanoscale. These differences can include, for example, one or more ofdouble-layer overlap (DLO) and its effect on electro-osmosis and chargepermselectivity, localized enhancement of electric fields, highersurface to volume ratios, confinement effects on large synthetic andbiopolymers, and the emerging importance of entropic effects. See, e.g.,Yuan et al., Electrophoresis 2007, 28, 595-610; Schoch et al., Rev. Mod.Phys. 2008, 80, 839-883; and Kovarik et al., Anal. Chem. 2009, 81,7133-7140.

Nanochannels are well suited for a number of applications includingsingle molecule detection and identification, confinement andmanipulation of biopolymers, biological assays, restriction mapping ofpolynucleotides, DNA sizing, physical methods of genomic sequencing, andfundamental studies of the physics of confinement. See, e.g., Riehn etal., Restriction mapping in nanofluidic devices. Proc. Natl. Acad. Sci.USA 2005, 102, 10012; Reccius et al., Conformation, length, and speedmeasurements of electrodynamically stretched DNA in nanochannels.Biophys. J. 2008, 95, 273; and Cipriany et al., Single moleculeepigenetic analysis in a nanofluidic channel. Anal. Chem. 2010, 82,2480. It is expected that the successful implementation of at least someof the potential applications will require the careful control ofmolecular dynamics within the nanochannels, including the velocity ofmolecular transport and the frequency with which analyte molecules aredriven through the nanochannels. The transport of a macromolecule frommacroscopic and microscopic reservoirs through nanofluidic conduits thatare smaller than the molecule's radius of gyration may require theapplication of a driving force (e.g., hydrodynamic, electrostatic,gravitational) to overcome an energy barrier. This barrier is primarilyentropic in nature and can derive from the reduction in the molecule'sconformational degrees of freedom in moving from free solution to theconfining nanochannel. See, Brochard et al., Dynamics of confinedpolymer chains. J. Chem. Phys. 1977, 67, 52, Additionally, theprobability of a successful transport event can be proportional to thelikelihood that the molecule collides with the entrance of thenanofluidic conduit in a conformation favorable to threading. See, Kumaret al., Origin of translocation barriers for polyelectrolyte chains. J.Chem. Phys. 2009, 131, 194903. The practical implication of thesefundamental conditions is that molecular transport does not occur untila finite threshold driving force is applied. The magnitude of therequisite force may be considerable, resulting in transport of theanalyte through the nanochannel at high velocity. The energy barrier canpreclude or inhibit successful transport of the analyte molecule atlower velocity through a nanochannel, such lower analyte velocities maybe desirable for many applications.

SUMMARY OF EMBODIMENTS OF THE INVENTION

Embodiments of the invention are directed to devices for fluidicanalysis which include at least one nanofunnel, related methods offabricating, use of the devices and analysis systems.

Some embodiments are directed to methods of forming a chip with fluidicchannels. The methods include: (a) forming at least one nanofunnel witha wide end and a narrow end into a planar substrate, the nanofunnelhaving a length, with width and depth dimensions that both vary over itslength; and (b) forming at least one nanochannel and/or microchannelinto the planar substrate at an interface adjacent the narrow end of thenanofunnel.

The forming can include milling the nanofunnel that can be carried outusing and/or can include defining an electronic patterning file, e.g., abitmap, stream file, or other computer aided design (CAD) format withdesired dimensions. The milling can be carried out using focused ionbeam (FIB) milling.

The forming of the at least one nanofunnel and the at least onenanochannel and/or microchannel can both be carried out during a singlemilling operation using an FIB milling device and a defined electronicpatterning file, e.g., bitmap, stream file, or other CAD format toseamlessly connect the nanochannel to the narrow end of the nanofunnel.

The nanofunnel width and depth dimensions can be formed so that theyvary in a defined geometric relationship (e.g., parabolic, convex,concave, linear, concatenated funnels) over substantially an entirelength of the nanochannel to alter a cross-sectional size of the funnelfrom the wide end to the narrow end. This change in size may be by atleast a factor of two and may vary by at least an order of magnitude.

The defined geometric shape can be a user-defined shape using anelectronic patterning file, such as bitmap, stream file, or other CADformat.

The at least one nanochannel can have substantially constant width anddepth and the narrow end of the nanofunnel can have width and depthdimensions that substantially match a respective width and depthdimension of an aligned corresponding nanochannel.

The nanofunnel can have a length that is (approximately) between about 1μm to about 100 μm.

The method can further include sealing a flat cover to the substrate todefine a nanofluidic chip adapted to analyze a molecule, such as abiopolymer that can include, for example, DNA molecules and/or proteins.

Other embodiments are directed to devices for analyzing nucleic acids orother molecules. The devices include a nanofluidic chip comprising aplurality of nanofunnels. The nanofunnels have smooth inner surfaces.Each nanofunnel has a wide end and a narrow end and varies (typicallygradually) in depth and width along its length. The nanofunnels can eachbe connected to a respective nanochannel and/or microchannel.

The nanofunnels, where formed by FIB milling, may have at least tracesof milling beam projectile material implanted in the nanofunnel innersurfaces.

The nanofunnels can have width and depth dimensions that both vary in a(e.g., user-defined) geometric relationship (e.g., parabolic, convex,concave, linear, concatenated funnels) over substantially an entirelength of a respective nanochannel to alter a cross-sectional size ofthe funnel by at least an order of magnitude from the wide end to thenarrow end.

The nanochannels can have a substantially constant width and depth, andthe narrow end of the nanofunnels have width and depth dimensions thatsubstantially match a respective width and depth dimension of acorresponding nanochannel.

The forming the nanofunnel step can be carried out by milling. Themethod can include, before milling the nanofunnel, providing anelectronic patterning file that defines dwell times at defined X and Ycoordinates to generate the nanofunnel width and depth dimensions overthe nanofunnel length. The providing can be carried out to generate ananofunnel configuration with dimensions with an associated exponent “α”defined by a power law (width, depth˜x^(α)), where x is an axialcoordinate and alpha is a positive number.

The nanofunnel can have a shape with a power law exponent α configuredas a function of axial position x, where y˜x^(α(x)). Here “y” isunderstood to represent either of the dimensions width or depth. In someembodiments, the width and depth may be defined by the same function ofx, yielding a nanofunnel with an aspect ratio (depth:width) of 1 alongits entire length. In other embodiments, the width and depth may bedefined by different functions of x, yielding a nanofunnel with anaspect ratio other than 1 (e.g., 0.1, 0.2, 0.5, 2, 4) along its entirelength or an aspect ratio that varies along the nanofunnel's length.

These power laws are exemplary of a variety of geometric relationshipsand are not exclusive functions defining nanofunnel patterning andforming.

The nanofunnel can have a shape defined by a concatenation of functions(y₁, y₂, y₃, . . . ) where the width and depth of the nanofunnel aredefined by y₁ between axial coordinates x₀ and x₁, by y₂ between axialcoordinates x₁ and x₂, by y₃ between axial coordinates x₂ and x₃, and soon. Each segment of the nanofunnel can be seamlessly or discontinuouslyconnected to its neighboring segments and the narrow end of thenanofunnel can be seamlessly connected to a corresponding alignednanochannel or microchannel. The concatenated nanofunnels can consist of2 to 10 segments in some embodiments or can form long fluidic conduitsconsisting of 10-100 or even up to hundreds or thousands of segments inother embodiments.

Still other embodiments are directed to methods of analyzing an analyte.The methods can include: (a) providing a chip with at least onenanofunnel that merges into a corresponding nanochannel; (b) applying afirst voltage to cause an analyte to flow into a fluid nanofunnel; then(c) applying a second smaller voltage to cause the analyte to flow intoa corresponding nanochannel; and (d) electronically or opticallyanalyzing the molecule in the nanofunnel and/or nanochannel.

The method may also include determining molecular identification of theanalyte, length of the analyte or localized functionalization mappingbased on data from the analyzing step.

The applying step can be carried out so that the flow in the nanochannelis at low velocity.

Yet other embodiments are directed to fluidic analysis systems foranalyzing (single) molecules. The systems include: (a) a fluidic chipcomprising a plurality of nanofunnels, each funnel merging into at leastone respective nanochannel; and (b) a control circuit in communicationwith the chip configured to (i) apply a first defined transport voltageto cause a molecule to enter at least one nanofunnel then (ii) apply adefined second transport voltage that is less than the first definedtransport voltage to cause the molecule to flow into a correspondingnanochannel.

The nanofunnel width and depth dimension can vary in a parabolicrelationship over substantially an entire length of the nanochannel toalter a cross-sectional size of the funnel by at least an order ofmagnitude from the wide end to the narrow end.

At least some of the nanochannels can have substantially constant widthand depth, and the narrow end of the nanofunnels can have width anddepth dimensions that substantially match a respective width and depthdimension of an aligned nanochannel.

The control circuit of the analysis system can be configured to applythe second transport voltage so that the molecule has a low velocityflow in the nanochannel.

Embodiments of the invention can be configured to allow drivingtransport at low velocity.

Embodiments of the invention are directed to methods of analyzing amolecule. The methods include: (a) providing a device with at least onenanofunnel; (b) flowably introducing a target molecule into thenanofunnel; (c) trapping the target molecule in the nanofunnel for atime to spatially localize the analyte molecule; and (d) analyzing theanalyte molecule in the nanofunnel.

The analyte can include a single DNA molecule. Low fields (E<E_(min))can momentarily trap DNA molecules but are insufficient to prevent theirdiffusive escape out of the nanofunnel and away from the nanochannel.Intermediate fields (E>E_(min), E<E_(c)) can stably trap the DNA in thenanofunnel with the position of the DNA molecule (x_(i) and x_(f))dependent on the magnitude of the electric field. High fields (E>E_(c))can transport the DNA into and through the nanochannel. Values of thefield strengths E_(min) and E_(c) are dependent on the shape and size ofthe nanofunnel and the size of the DNA molecule.

Embodiments of the invention are directed to a Focused Ion Beam (FIB)milling system. The system includes a FIB milling apparatus incommunication with or comprising at least one electronic patterning fileconfigured to generate a nanofunnel in a target substrate.

The FIB milling apparatus is configured to generate any, some or all ofthe nanofunnel shapes described and/or claimed herein.

Embodiments of the invention can be carried out to evaluate DNA. Themethod includes obtaining a time-series of images of a single moleculeof fluorescently-stained λ-phage DNA fed through a nanofunnel into ananochannel having a depth dimension that is between about 0.5 nm toabout 10 nm, typically between about 1 nm to about 5 nm (e.g., about 3nm).

It is noted that aspects of the invention described with respect to oneembodiment, may be incorporated in a different embodiment although notspecifically described relative thereto. That is, all embodiments and/orfeatures of any embodiment can be combined in any way and/orcombination. Applicant reserves the right to change any originally filedclaim and/or file any new claim accordingly, including the right to beable to amend any originally filed claim to depend from and/orincorporate any feature of any other claim or claims although notoriginally claimed in that manner. These and other objects and/oraspects of the present invention are explained in detail in thespecification set forth below. Further features, advantages and detailsof the present invention will be appreciated by those of ordinary skillin the art from a reading of the figures and the detailed description ofthe preferred embodiments that follow, such description being merelyillustrative of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a fluidic analysis device with afunnel-shaped entrance to a nanochannel at one end that intersects orcontacts a microchannel used for sample introduction on the other endaccording to embodiments of the present invention.

FIG. 2 is a schematic illustration of a fluidic analysis device with aplurality of spaced apart nanochannels and respective funnel-shapedentrances according to embodiments of the present invention.

FIG. 3A is a grayscale bitmap image used to pattern a funnel accordingto embodiments of the present invention.

FIG. 3B is a top view SEM image of the funnel and nanochannel milledinto a quartz substrate using the bitmap shown in FIG. 3A according toembodiments of the present invention.

FIG. 3C is a tilted end perspective (about 52 degrees) view of thefunnel and nanochannel shown in FIG. 3B illustrating the funnel candecrease in size (width and depth as it approaches the nanochannel.

FIGS. 4A-4C are schematic illustrations of sizing, mapping andsequencing using a prior art nanochannel.

FIGS. 5A and 5B are schematic illustrations comparing DNA transport intonanochannels with (FIG. 5B) and without (FIG. 5A) the use of a funnelaccording to embodiments of the present invention.

FIG. 6A is a schematic illustration of a fabrication sequence thatincludes etching, milling and bonding to fabricate a fluidic analysisdevice according to embodiments of the present invention.

FIG. 6B is a schematic exploded view illustration of a device withstacked substrates according to embodiments of the present invention.

FIGS. 7A-7C are pairs of schematic illustration with corresponding (SEM)images of different exemplary geometric shaped funnel contours accordingto embodiments of the present invention.

FIG. 8A is a front view of a milling apparatus with an FIB milling modewhere each pixel defines where and for how long an ion beam dwells onthe substrate according to embodiments of the present invention.

FIG. 8B is a graph of actual depth (nm) versus dwell time for ion beamsinto substrates that can be used to create nanofunnels according toembodiments of the present invention.

FIG. 9A is a front perspective view of a fluorescence microscope withstained DNA added to reservoirs for fluidic electrokinetic transportthrough the nanochannels and transport events can be observed usingfluorescence microscopy (with the circle inset showing a magnified viewof the nanochannel array) according to embodiments of the presentinvention

FIG. 9B is an image of a series of frames showing transport offluorescently-stained λ-DNA molecules through a single nanochannel witha funneled entrance according to embodiments of the present invention.

FIGS. 10A-10C are schematic illustrations of nanofunnels and DNAtransport at different field strengths according to embodiments of thepresent invention.

FIG. 11A is a schematic illustration of a nanofunnel with a symmetryaxis and dimensional parameters for evaluating suitable electric fieldsfor transport or trapping for various geometries according toembodiments of the present invention.

FIG. 11B is a schematic illustration of different funnel geometries withassociated “α” characteristics between 0 and 4 according to embodimentsof the present invention.

FIGS. 11C and 11D are graphs of ln V versus ln x for α<0.5 (FIG. 11C)and α>0.5 (FIG. 11D) according to embodiments of the present invention,

FIG. 11E is a schematic illustration of a nanofunnel that has dimensionsdefined by the proportionality y˜x^(α(x)), where the exponent “α” isitself a function of the axial position x according to embodiments ofthe present invention.

FIGS. 11F and 11G are schematic illustrations of nanofunnels that havemultiple segments (also called multiple portions) where the dimensionsin each segment or portion are defined by a different geometricrelationship and where neighboring segments or portions are connectedseamlessly (FIG. 11F) or discontinuously (FIG. 11G).

FIGS. 12A and 12B are graphs of ln c versus ln x for α<0.5 (FIG. 12A)and α>0.5 (FIG. 12B) with associated exemplary respective nanofunnelsholding DNA according to embodiments of the present invention.

FIG. 13A is a graph of x_(i)/b versus qE_(o)D/kT of theory (lines) andsimulation results (markers) describing the position of a DNA molecule'sleading end (x_(i)) as a function of applied voltage (proportional toE₀, the electric field magnitude in the nanochannel) with valuesnormalized and plotted as dimensionless variables where b is thecharacteristic DNA Kuhn length, q is the charge on the DNA, D is thegeometric average of the nanochannel width and depth, k is Boltzmann'sconstant, and T is temperature for two different DNA molecule lengthsaccording to embodiments of the present invention.

FIG. 13B is a graph similar to that shown in FIG. 13A but showing thetrailing end (x_(f)) according to embodiments of the present invention.

FIG. 14 is a graphical comparison of theory and simulations describingthe dependence of the critical electric field required to drivetransport through the nanochannel on the power law exponent, α,according to embodiments of the present invention. The dimensionlessvariable of the plot ordinate is the critical field with the nanofunnelE_(c) ^(f), normalized by the critical field necessary to drivetransport through a nanochannel with no funnel, E_(c).

FIG. 15A is a bright field optical image of an exemplary nanofunnel usedfor a trapping experiment for DNA according to embodiments of thepresent invention.

FIG. 15B is a fluorescence image of a stained DNA molecule that isstably trapped in the exemplary nanofunnel shown in shown in FIG. 15A

FIG. 15C is a line profile graph of intensity versus x (μm) created fromthe fluorescence image in FIG. 15B and used to determine the position ofthe DNA molecule.

FIG. 15D is an image compiled of a series of frames similar to thatshown in FIG. 15B, where for each experimental condition (e.g., voltage,DNA length, funnel shape), greater than 20 minutes of data was recordedand position and length information extracted using an analysis programaccording to embodiments of the present invention.

FIG. 16 is a graph of experimentally determined position x_(o) versusvoltage (V) for DNA as shown by the appended image of the DNA in thenanofunnel according to embodiments of the present invention.

FIG. 17 is a graph of experimentally determined position x_(o) versusvoltage (V) for DNA for lambda (λ) and T4 DNA with and without PVP(polyvinylpyrrolidone) according to embodiments of the presentinvention.

FIG. 18 is a graph of experimentally determined length changes (lengthversus x_(o)) at various voltages for lambda and T4 DNA with and withoutPVP according to embodiments of the present invention.

FIG. 19 are schematic illustrations of a nanofunnel that merges into thenanochannel with DNA and two alternate drive directions and eventfrequency according to embodiments of the present invention.

FIG. 20 is a graph of experimentally determined event frequency (min⁻¹)versus voltage (V) with a portion exploded for ease of reference with anappended schematic of the drive direction (funnel side and channel side)according to embodiments of the present invention.

FIG. 21 is an image of a nanochannel illustrating DNA and itsconcentration at the nanochannel entrance when a voltage less than theenergy barrier is applied for a period of time (V=0.5V after about 1.5hours) according to embodiments of the present invention,

FIG. 22A is an atomic force microscopy image of a funnel interfaced to ananochannel in which nanofunnel depth is measured at each position whosecoordinates correspond to width and length according to embodiments ofthe present invention.

FIG. 22B is a graph of dimensions (depth, width and area) versus lengthaccording to embodiments of the present invention. The measurements ofthe funnel can be made using the image of FIG. 22A and thecross-sectional area of the funnel can vary linearly along its length.

FIG. 23A is an AFM (atomic force microscopy) image of a funnel withα=0.5 according to embodiments of the present invention.

FIG. 23B is a bit map (BMP) image used to pattern the interface shown inFIG. 23A.

FIG. 23C is an SEM (scanning electron microscope) image of the interfaceshown in FIG. 23A.

FIG. 24 is a graph of depth, width (μm) versus length x (μm) ofexemplary funnel geometry according to embodiments of the presentinvention.

FIG. 25 is a set of AFM images for funnels having different values of αaccording to embodiments of the present invention.

FIG. 26A is a graph illustrating a comparison between calculated(theoretical) and experimentally determined positions of the leading andtailing ends of a trapped λ-phage DNA molecule according to embodimentsof the present invention.

FIG. 26B is a similar graph illustrating a comparison between calculated(theoretical) and experimentally determined positions of the leading andtailing ends of a trapped T4-phage DNA molecule according to embodimentsof the present invention.

FIG. 27 is a schematic illustration of an analysis device/system using asubstrate with at least one fluidic nanofunnel and associated channelaccording to embodiments of the present invention.

FIG. 28 is a schematic illustration of a milling apparatus incommunication with and/or including an electronic patterning file forforming desired nanofunnel structures according to embodiments of thepresent invention.

DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The present invention will now be described more fully hereinafter withreference to the accompanying figures, in which embodiments of theinvention are shown. This invention may, however, be embodied in manydifferent forms and should not be construed as limited to theembodiments set forth herein. Like numbers refer to like elementsthroughout. In the figures, certain layers, components or features maybe exaggerated for clarity, and broken lines illustrate optionalfeatures or operations unless specified otherwise. In addition, thesequence of operations (or steps) is not limited to the order presentedin the figures and/or claims unless specifically indicated otherwise. Inthe drawings, the thickness of lines, layers, features, componentsand/or regions may be exaggerated for clarity and broken linesillustrate optional features or operations, unless specified otherwise.In some schematic illustrations, a nanofunnel may be depicted as atwo-dimensional projection to clearly depict the nanofunnel shape. Itshould be understood that width and depth dimensions can both vary overthe nanofunnel's length.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms, “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises,”“comprising,” “includes,” and/or “including” when used in thisspecification, specify the presence of stated features, regions, steps,operations, elements, and/or components, but do not preclude thepresence or addition of one or more other features, regions, steps,operations, elements, components, and/or groups thereof. As used herein,the term “and/or” includes any and all combinations of one or more ofthe associated listed items. As used herein, phrases such as “between Xand Y” and “between about X and Y” should be interpreted to include Xand Y. As used herein, phrases such as “between about X and Y” mean“between about X and about Y.” As used herein, phrases such as “fromabout X to Y” mean “from about X to about Y.”

It will be understood that when a feature, such as a layer, region orsubstrate, is referred to as being “on” another feature or element, itcan be directly on the other feature or element or intervening featuresand/or elements may also be present. In contrast, when an element isreferred to as being “directly on” another feature or element, there areno intervening elements present. It will also be understood that, when afeature or element is referred to as being “connected”, “attached” or“coupled” to another feature or element, it can be directly connected,attached or coupled to the other element or intervening elements may bepresent. In contrast, when a feature or element is referred to as being“directly connected”, “directly attached” or “directly coupled” toanother element, there are no intervening elements present. Althoughdescribed or shown with respect to one embodiment, the features sodescribed or shown can apply to other embodiments.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this invention belongs. It will befurther understood that terms, such as those defined in commonly useddictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the present applicationand relevant art and should not be interpreted in an idealized or overlyformal sense unless expressly so defined herein. Well-known functions orconstructions may not be described in detail for brevity and/or clarity.

Spatially relative terms, such as “under”, “below”, “lower”, “over”,“upper” and the like, may be used herein for ease of description todescribe one element or feature's relationship to another element(s) orfeature(s) as illustrated in the figures. It will be understood that thespatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the figures. For example, if the device in thefigures is inverted, elements described as “under” or “beneath” otherelements or features would then be oriented “over” the other elements orfeatures. Thus, the exemplary term “under” can encompass both anorientation of over and under. The device may be otherwise oriented(rotated 90 degrees or at other orientations) and the spatially relativedescriptors used herein interpreted accordingly. Similarly, the terms“upwardly”, “downwardly”, “vertical”, “horizontal” and the like are usedherein for the purpose of explanation only unless specifically indicatedotherwise.

It will be understood that, although the terms first, second, etc. maybe used herein to describe various elements, components, regions, layersand/or sections, these elements, components, regions, layers and/orsections should not be limited by these terms. These terms are only usedto distinguish one element, component, region, layer or section fromanother region, layer or section. Thus, a first element, component,region, layer or section discussed below could be termed a secondelement, component, region, layer or section without departing from theteachings of the present invention.

The term “about” refers to a dimension or other parameter that is closeto but not exactly the associated dimension or other parameter value ornumber, typically within about +/−20% or less, such as about +/−10% orless, than that dimension or other parameter value or number.

The term “gradually” with respect to a change in shape of a respectivenanofunnel according to some particular embodiments refers to a shapethat tapers inward to a smaller size.

Generally stated, embodiments of the application provide techniquesusing milling to fabricate nanofunnels, and optionally nanochannels,with primary (sometimes described as “critical”) dimensions. The term“milling” refers to any process that forms channels using a chargedparticle or particles. Thus, while some examples are described hereinwith respect to a Focused Ion Beam (FIB) milling process, other millingprocesses may be used including those that employ Ar⁺ ion beams, protonbeams, He⁺ ion beams, Ga⁺, In⁺, C₆₀ ⁺, and electron beam milling. Theterm “implanted projectiles” refers to the particles implanted in thesubstrate nanofunnels or nanochannels in response to the milling process(based on the type of beam used to form the nanochannel). In someembodiments, devices used to analyze (fluidic) samples can compriseimplanted projectiles that may be present in a trace amount (detectablewith SEM or other evaluation methods), present in larger amounts orremoved (e.g., via known subsequent processing techniques). The millingcan be carried out to alternate charged particle milling with chargedparticle induced deposition processes that allows redeposition ofmasking material during the milling process. The redeposition of maskingmaterials can allow for a renewal of the masking material during theetching process enabling greater aspect ratio nanochannels to beproduced. The deposition of solid phase materials using focused particlebeams and volatile precursor molecules is a well-established technique.(see S. J. Randolph, et al., Crit. Rev. Solid State Mat. Sci., 2006, 31,55-89, the contents of which are hereby incorporated by reference as ifrecited in full herein.) A broad range of metals, insulators, andsemiconductor materials can be deposited using these technique includingCr, Pt, Si and/or SiO₂. The redeposition process may be particularlyimportant when milling the narrowest high-aspect ratio funnels and/orchannels. These funnels and/or channels can be milled by rastering thecharged particle beam across an area and/or along a line. Precursor gasof the deposited material can be injected at appropriate intervalsduring the beam rastering to achieve the desired nanochannel dimensions.

The term “electronic patterning file” refers to electronic(programmatic) instructions typically held in one file, but may bedistributed in more than one file and on local or remote computers, todefine a target nanofunnel formation pattern or image that can be usedfor a fabrication device such as for a milling mode of a millinginstrument. The electronic patterning file can comprise one or more CAD(computer-aided design) files with milling instrumentinstructions/controls as to ion beam dwell time and intensity and thelike. The term “bitmap” refers to computer-implemented instructions of adesired milling pattern or image for a milling mode for a millinginstrument, such as an FIB milling instrument, where each pixel defineswhere and for how long an ion beam dwells on a target substrate. Theterm “stream file” refers to an ASCII text or binary file that definesthe ion beam dwell time for each of a set of x, y coordinates (pixels),as listed in the file. As will be recognized by one of skill in the art,the functionality of the bitmap and stream file is the same but a bitmapis a matrix while the stream file is a list which can have subtledifferences as to how the instrument patterns from the respective files.

It is noted that while the following examples describe the use ofmilling, and particularly, FIB milling, to form the nanofunnel, thenanofunnel and/or nanochannel (or microchannel) can be formed using anysuitable apparatus or fabrication technology including for examplemilling, etching, molding, and embossing or combinations of thedifferent fabrication technologies. For example, a first complementaryfeature can be formed, e.g., etched or milled on/in a target substrate,then the funnel construct can be formed by molding or embossing over orabout the complementary feature.

The term “power law” refers to a mathematical model of nanofunnel shapeand dimensions characterized by an exponential factor “alpha” where thenanochannel width (w) and depth (d) vary with position along thenanofunnel's longitudinal axis (x) by the power law w, d˜x^(α). Thispower law may sometimes be described as y˜x^(α), where it is understoodthat “y” represents the width and/or depth of the nanofunnel. The widthand depth may be defined by the same function of x, yielding ananofunnel with an aspect ratio (depth:width) of 1 along its entirelength. The width and depth may be defined by different functions of x,yielding a nanofunnel with an aspect ratio other than 1 (e.g., 0.1, 0.2,0.5, 2, 4) along its entire length or an aspect ratio that varies alongthe nanofunnel's length. The power laws described herein are exemplaryof a variety of geometric relationships and are not exclusive functionsdefining nanofunnel patterning and forming.

The term “nanofunnel” refers to a fluidic channel that has athree-dimensional funnel shape with two opposing ends, with one endhaving a wide end with a wider opening and the other opposing narrow endhaving a narrower opening, with the narrow end having at least oneprimary dimension (width and/or depth) with a nanometer size. The funnelshape may be substantially conical or frustoconical, concave or convex,but is typically formed in one or two overlying, cooperating flatsubstrates so that the funnel depth and width taper inward to narrow inwidth and also to become more shallow in depth along one direction,which may be in a flow or reverse flow direction. In some embodiments,the funnel shape can be configured to gradually decrease incross-sectional size by at least an order of magnitude along the transitpath, with the smallest dimensions being substantially equal to those ofa nanochannel with which they can be seamlessly integrated (and mergeinto). The term “primary dimension” in the singular refers to a widthand/or depth dimension with the term used in the plural to include boththe width and depth dimensions. The primary dimensions of the nanofunnelat the narrow end are both typically below about 50 nm, including about25 nm or less (on average or at a maxima), such as between about 1 nm toabout 25 nm and any value therebetween, including about 5 nm, about 10nm, about 15 nm, about 20 nm and about 25 nm. The length of thenanofunnel(s) can vary typically according to end application. Theseapplications can include, for example, but are not limited to, a devicethat includes a nanofunnel that merges into a nanochannel, a device thatincludes a nanofunnel that connects a nanochannel with a microchannel, adevice that has a nanofunnel that joins two closely spaced apartmicrochannels, or a device that has a nanofunnel in fluid communicationwith a microreservoir.

The term “nanochannels” refers to an elongate channel with sidewalls anda floor, sometimes also referred to as a “trench”. The term“microchannels” refers to channels that are small but larger thannanochannels. The primary dimensions of the nanochannel(s) are bothtypically below about 10 nm, including about 5 nm or less (on average orat a maxima). In some embodiments, the depth and/or width can be about 3nm or less, e.g., about 1 nm. In some embodiments, the depth is betweenabout 1 nm to about 10 nm (on average or at a maxima) and the width isthe same or larger (e.g., between about 2-10 times larger) than thedepth dimension, again either measured on average or as a maxima. Inother embodiments, the nanochannel can have primary dimensions up toabout 100 nm. The length of the nanochannels can vary typicallyaccording to end application. However, in some embodiments thenanochannels can have a relatively short length such as about 100 nm,but are typically between about 10 microns to 100 microns. In otherembodiments, the nanochannels can be longer, such as between about0.5-12 inches (particularly when using stitching or continuous preciselycontrolled movements of a sample stage while milling), although are moretypically between about 0.5-2 inches. The nanochannels may be linear orextend along an axis in a spiral, serpentine or other curvilinearpattern.

The nanofunnel(s) and, where used, nanochannels, can be formed into atleast one solid planar substrate to have an open top surface and aclosed bottom surface with the sidewalls extending therebetween. A covermay be used to seal or otherwise close the upper surface of thenanofunnel and nanochannel. The nanochannels can be configured with anaspect ratio (AR) of about 1 (e.g., the average width and average depthare substantially the same or do not vary more than about 20%) but mayalso have other aspect ratios, typically with the width dimension being2-10 times greater than the depth dimension, e.g., such as an AR ofabout 1:3 (H (depth dimension):W). In some embodiments, the nanochannelscan include aspects greater than 1, but less than 10.

The term “low velocity” refers to a velocity associated with movement ofa sample, e.g., single molecule, through a nanochannel at velocitiesbelow about 0.01 cm/s. The term “low voltage driving force” refers tothe voltage applied using electrodes in communication with a flowtransit channel to drive transport of a sample, e.g., a molecule, intoand/or through a respective nanofunnel and/or nanochannel. The lowvoltage driving force can be described in absolute terms or in terms oflength of a fluid channel, e.g., nanochannel or nanofunnel. The lowvoltage driving force for a nanofunnel, where used, can be under about5V, typically under about 1V, and for a nanochannel can be lower such asabout 500 mV or less. Typically, one driving voltage is applied to drivea sample into a respective nanofunnel, typically between about 1-5V,then a smaller second voltage can be applied to move the sample into ananochannel, the second voltage typically being below about 500 mV, suchas, for example, between about 300 mV to about 200 mV.

Turning now to the figures, FIG. 1 is a schematic illustration of oneembodiment of a device 10. As shown, the device 10 has a planarsubstrate 10 p with a microchannel 15, a nanofunnel 20 and a nanochannel30. In the embodiment shown, the nanofunnel 20 has a narrow end 20 nthat defines a funnel-shaped entrance into a respective alignednanochannel 30. The wide end of the funnel 20 w can reside proximate amicrochannel used for fluidic sample introduction. The nanochannel 30can have a length that is much greater than the length of the funnel 20,typically at least three times greater and more typically greater thanabout 5 times, 6 times, 7 times, 8 times, 9 times, 10 times or evengreater length. In some embodiments, the nanofunnels 20 can have arelatively short length such as about 100 μm or less, typically betweenabout 100 nm to about 50 μm, including about 75 μm, about 50 μm, about25 μm, about 15 μm, about 10 μm, about 1 μm, about 500 nm, and about 100nm or any number therebetween. In some embodiments, the length can beless than 100 nm, such as about 75 nm, about 50 nm, about 25 nm or lessand any number therebetween.

Referring to FIG. 2, the device 10 can include at least one nanofunnel20, but typically includes a plurality of spaced apart nanofunnels 20.Although shown as two spaced apart nanofunnels 20 ₁, 20 ₂, the device 10can include more than two nanofunnels. As shown, each nanofunnel 20 ₁,20 ₂ can merge into a respective nanochannel 30 ₁, 30 ₂ or connect otherfluid structures.

The nanofunnel 20 can be configured to have dimensions in both width anddepth (also described as “height”) that gradually decrease by over atleast an order of magnitude along the transit path. In some embodiments,the narrow end 20 n with the smallest dimensions can be substantiallyequal to and aligned with those of a corresponding nanochannel 30 withwhich they can be (seamlessly) integrated.

FIG. 3A is a grayscale bitmap image used to pattern a funnel withgradually varying width and depth over its length 20 l. FIG. 3B is a topview SEM (Scanning Electron Microscope) image of a funnel 20 and a firstend of a corresponding nanochannel 30 milled into a quartz substrateusing the bitmap 20 bm shown in FIG. 3A. FIG. 3C is a top, endperspective view (tilted at 52 degrees) of the funnel and nanochannelshown in FIG. 3B illustrating the varying depth (in the lengthdirection). In this embodiment, the funnel 20 decreases in size fromabout 1.5 μm×about 1.5 μm (width×depth) to about 25 nm×about 25 nm(width×depth). However, other funnel geometry and dimensions may beused.

In some embodiments, the funnels 20 can be configured to lower thethreshold force needed to drive transport. This can be achieved by thegradual increase in the degree of confinement experienced by an analytemolecule as it moves along the length of the funnel 20. This effect, incombination with a force gradient that may partially be attributed tothe funnel geometry, can effectively “precondition” the analytemolecule, resulting in a conformation conducive to threading into thenanochannel 30.

FIGS. 4A-C and 5A illustrate a nanochannel 30 with a fluid reservoir 60with an analyte 40 (DNA), and without a funnel 20, which can be used formapping, sizing and sequencing DNA. See also, Levy et al., Chem Soc Rev39 2010, 1133; Lagerqvist et al., Nano Lett, 6 2006, 779, and U.S.Provisional Application Ser. No. 61/384,738, filed Sep. 21, 2010 (andcorresponding pending PCT/US2011/052127) the contents of which areincorporated by reference as if recited in full herein. FIG. 5Billustrates the device 10 with the nanofunnel 20 that can provide anentry path for the analyte 40.

FIG. 6A illustrates a series of operations (A-C) that can be used toform devices 10 with at least one funnel 20 using milling, typically FIBmilling. It is noted that the sequence of A and B may be reversed. Theplanar substrate 10 p of the device 10 funnel(s) 20 can be processed toinclude one or more microfluidic channels 15 that can be prepared usingstandard photolithographic and etching techniques or other techniques(operation “A”). Next, FIB milling can be used to form an interface witha funnel 20 and nanochannel 30 in the substrate 10 p. The funnel andnanochannel 20, 30 can be seamless and connect to the channels 15 to bein fluid communication with the channels 15 and reservoirs 60 (operation“B”).

The device 10 can be a compact “chip”-like device with multiplenanofunnels 20 and nanochannels 30 and one or more associated reservoirs60. The reservoir(s) 60 may have a short cylindrical configuration orother configuration and may be externally accessible (FIG. 6A). The term“chip” refers to a substantially flat compact body with integratedfluidic structures. The chip can be any geometric shape but is typicallypolygonal, such as substantially square or substantially rectangular.The chip can be in different sizes but typically has an area that isless than about 10 in² (e.g., about 25 mm×25 mm).

FIG. 6A also illustrates that electrodes 70 can be attached to thedevice 10, typically with positive and negative polarity at spaced apartrespective reservoirs 60 to drive the transport of the fluid analyte(e.g., molecule) through the fluidic structures as is well known.

In some embodiments, the device 10 can be configured for analyzingmolecules, such as nucleic acids. The device 10 can be a nanofluidicchip comprising a plurality of nanofunnels 20, each connected to arespective nanochannel 20. The nanofunnels 20 and nanochannels 30 canhave a smooth inner surface (from the milling process into thesubstrate). The nanofunnels 20 and the nanochannels 30 can include atleast traces of implanted milling projectiles from a milling beam usedto form the nanofunnels 20 and the nanochannels 30. The interfacebetween a respective nanofunnel 20 and channel 30 can be seamless inthat the narrow end of the funnel 20 can have the same dimensions as thenanochannel 30. The nanochannel 30 can have a constant width and depthover at least a major portion of its length and typically over itsentire length. The nanochannel 30 can be formed during a single millingoperation as continuation of the milling process used to form thenanofunnel 20 or vice versa (e.g., the nanochannel can be formed firstand the nanofunnel can be a continuation of that process). The term“seamless” means that there is not a seam that adjoins the two features.

The device 10 can have a planar substrate 10 p of a variety of substratematerials, allowing device fabrication in glass, quartz, silicon,ceramics, metals, plastics, etc. In the case of electrically insulatingsubstrate materials, FIB milling can be performed through a relativelythick (>100 nm) high quality metal film deposited on the top surface ofthe substrate. This metal film prevents charging during the millingprocess and allows milling of features with suitable tolerances and canallow critical dimensions that extend below 5 nm. See, e.g., U.S.Provisional Application Ser. No. 61/384,738, filed Sep. 21, 2010 andcorresponding pending PCT/US2011/052127, and Menard, L. D.; Ramsey, J.M., The fabrication of sub-5-nm nanochannels in insulating substratesusing focused ion beam milling. Nano Lett. 2011, 11, 512, the contentsof which are incorporated by reference as if recited in full herein.

FIGS. 7A-7C illustrates different exemplary geometric shaped funnelcontours 20 c. FIG. 7A illustrates that the nanofunnel 20 has a convexcontour 20 cv. FIG. 7B illustrates the funnel 20 has a straight linetaper with walls tapering in at a (substantially) constant slope. FIG.7C show a nanofunnel 20 with a concave contour 20 con. FIG. 23illustrates that the nanofunnel 20 can have a substantially parabolicrelationship/shape.

At “B”, nanochannels 30 of a substantially constant depth can befabricated by rastering the ion beam over a rectangular area or along aline, with each point in the rectangle or line exposed to the same iondose. Deeper (funnel) channels can be milled by defining higher iondoses while shallower channels can be milled using lower ion doses. FIG.8A shows an example of an FIB milling device with a BMP milling modewhere each pixel can define where and how long an ion beam dwells on thesubstrate 10 p. FIG. 8B illustrates an example of depth (nm) that can beset by dwell time (typically between about 1 μs to about 10 ms perpixel) with an appended gray scale graduated graph of dwell timeresulting in increased depth. Because FIB milling is a direct writeprocess, features that are relatively complex can be patterned, asdescribed below. After FIB milling and removal of the metal film fromthe substrate (if used), the fluidic network comprising a funnel 20 canbe sealed by bonding a cover plate 50 (operation “C”) on top of thesubstrate using one of several possible methods such as fusion, anodic,or adhesive bonding.

In the embodiment shown in FIG. 6A, the use of two planar cooperatingsubstrates results with the funnel formed only in the bottom substrate10 p results in a flat top face to the funnels 20, regardless of thegeometry milled into the substrate 10 p. FIG. 6B shows an embodimentwhere the funnels 20 can be configured so that both width and depth varygradually and symmetrically around the long axis of the funnel 20. Thisconfiguration can be fabricated by milling identical funnel features andoptionally a portion or all of the nanochannel 30, in both the top andbottom substrates 50, 10 p, followed by bonding of the two substrateswith precise alignment.

It is noted that prototypes of the device 10 were fabricated in quartzsubstrates because of quartz's suitability for microfluidic andnanofluidic devices. However, FIB milling of nanofluidic structures canbe extended to various hard and soft materials as described in the U.S.Provisional Application Ser. No. 61/384,738, filed Sep. 21, 2010 andcorresponding pending PCT/US2011/052127, which has been incorporated byreference. Examples of hard materials include, but are not limited to,substrates comprising one or combinations of: glass, quartz, silicon,and silicon nitride. The soft materials can have a low Young's Modulusvalue. For example, elastomers and harder plastics and/or polymers canhave a range between about 0.1-3000 MPa. Examples of soft materialsinclude, but are not limited to, polydimethylsiloxane (PDMS),polymethylmethacrylate (PMMA), and polyurethane.

As shown in FIG. 8A, a milling apparatus 200 can be configured togenerate a desired shape of a nanofunnel 20 in a substrate 10. Anelectronic patterning file 200 f (which can be provided in a number ofmanners including, for example, by one or more of an ASIC (ApplicationSpecific Integrated Circuit), an application (“APP”), a module and/orsubdirectory file of a controller or digital signal processor) that canbe held in the milling apparatus 200 or the milling apparatus 200.Alternatively, the apparatus 200 can be controlled or have access to atleast one external (local or remote) device such as a processor with theelectronic patterning file 200 f that can generate a desired funnelshape in the substrate 10. The electronic patterning file 200 f can alsobe distributed over various components and locations. The electronicpatterning file 200 f can define the dwell time per pixel of the millingbeam 200 b (FIG. 8B) over X, Y coordinates, or other defined coordinatesystems to generate a defined nanofunnel shape. The electronicpatterning file 200 f can be configured as selectable differentpatterning instructions correlated to one or more of the following: (i)different substrate materials; (ii) different nanofunnel shapes and/ordimensions; or (iii) different target analytes.

The milling apparatus 200 can include a control circuit 200 c that cancommunicate with at least one remote or local processor via a local areanetwork (LAN), a wide area network (WAN) or via a global computernetwork, e.g., the Internet to obtain or use the electronic patterningfile 200 f. The milling apparatus 200 can be an FIB milling apparatus.

As shown in FIG. 28, a fabrication system 201 can comprise the apparatus200 can include a control module or circuit 200 c that can be onboardthe apparatus or at least partially remote from the apparatus. If thelatter, the control module or circuit 200 c can reside totally orpartially on a server 225 (FIG. 28). The server 225 can be providedusing cloud computing which includes the provision of computationalresources on demand via a computer network.

Referring to FIGS. 8A and 8B, according to some embodiments, FIB millingcan be performed using a Helios NanoLab DualB earn Instrument (FEICompany) with a Ga⁺ ion source operated at about 30 kV. This instrumentis capable of using bitmap image files (20 bm, FIG. 5A-7C) to define amilling pattern. The x and y coordinates of the image define where theion beam dwells during the scan, thus achieving milling, and thegray-scale value of the pixel (0 to 255) defines the length of time thatthe ion beam dwells on the region of the sample corresponding to thepixel. The operator or a default configuration of the apparatus 200and/or the electronic patterning file 200 f can define the maximum dwelltime, t_(max). White pixels (gray-scale value equal to 255) can beexposed for a milling time of t_(max) while black pixels (gray-scalevalue equal to 0) are not exposed to the ion beam and thus are notmilled. Pixels with intermediate values on the gray scale can be milledfor a fraction of t_(max), where the length of exposure is linearlydependent on the gray-scale value (e.g., the dwell time at a pixel witha gray-scale value of 125 is 125/255*t_(max)=0.49*t_(max)). Color scalepixels may be used in the future.

FIGS. 3B-3C show representative scanning electron microscopy (SEM)images of a funnel with varying depth and width interfaced to ananofluidic channel. As discussed above, FIG. 3A is an image of theoriginal bitmap file 20 bm used to mill the funnel and channel featuresshown in FIGS. 3B and 3C.

Measuring the Electrophoretic Mobility of DNA in 25-nm Nanochannels

A series of experiments were carried out to determine theelectrophoretic mobility of double-stranded DNA through 50-μm longchannels having dimensions of 25 nm×25 nm (width×depth). These consistedof electrokinetically driving single λ-phage DNA molecules from onemicrofluidic reservoir to another through an array of nanochannels (FIG.9A). FIG. 9A is a schematic illustration that shows an experimentalsetup where stained DNA solutions are added to the device reservoirs 60,DNA is electrokinetically driven via electrodes and electric field(s)through the nanochannels 30, and transport events are observed usingfluorescence microscopy using a microscope 230. The inset shows amagnified view of the nanochannel array. The DNA was stained with anintercalating fluorescent dye (YOYO-1, Invitrogen) at a base pair to dyemolecule ratio of 5:1. Fluorescence was excited by light from a mercuryarc lamp passing through an excitation filter and a 100× oil-immersionplan apochromatic objective lens. Fluorescence from single molecules wascollected through the 100× lens and imaged using an electron-multiplyingCCD camera (Cascade II, Photometrics). This high sensitivity camera cancollect images at frame rates up to 400 frames per second. Imageanalysis of individual, time-stamped frames provided information onsingle molecule dynamics such as molecular extension and the velocity oftransport.

However, it was found that initiating translocation of the DNA moleculesthrough nanochannels of this size required electric field strengths inthe nanochannels of at least 1000 V/cm. In practice, field strengthsexceeding 3000 V/cm were required to drive events with sufficientfrequency to analyze a statistically significant sample of molecules.This corresponded to a velocity of ˜0.9 cm/s, meaning that duringtranslocation of the molecule through a 50-μm long nanochannel, fewerthan three frames were captured. This limited data, in combination withthe finite length of the λ-DNA molecules (˜20 μm when stained) and thepotential for image artifacts caused by the molecules' high velocityprecluded the determination of electrophoretic mobility.

In order to lower the threshold field strength to initiate the threadingof single DNA molecules into the about 25 nm×25 nm channels, a devicewith nanochannels having identical critical dimensions but with funneledentrances was fabricated. The funnel cross-section gradually decreasedin size from about 350 nm×350 nm to 25 nm×25 nm over a length of about 5μm. The change in width and depth can be defined by a parabolic function(FIG. 7C). An SEM image of one of these nanochannel entrances is shownin the inset in FIG. 9B (top right of the figure). The threshold fieldstrength (in the nanochannels) required to drive DNA translocationthrough the nanochannels in this device was about 350 V/cm, orthree-fold lower than the device without funneled entrances.Consequently, it was possible to record a greater number of frames for asingle translocation event and analyze these frames to determine thedynamics of transport. A representative series of frames showingtransport through one of the 25-nm nanochannels with a funneled entranceis shown in FIG. 9B. Here, it is clear that the DNA molecule enters intothe funnel where it slowly elongates into a configuration that thenthreads into the 25-nm nanochannel. In the absence of the confiningfunnel and at a comparable field strength, this threading process wouldlikely progress too slowly to ensure translocation before the DNAmolecule diffused away from the nanochannel entrance.

FIG. 9B illustrates a series of frames showing the transport offluorescently-stained λ-DNA molecules through a single 25-nm nanochannelwith a funneled entrance. The inset SEM image shows the entrance of thisnanochannel. The vertically oriented dashed lines indicate, from left toright, the entrance to the funnel, the funnel to nanochannel interface,and the other end of the nanochannel 30.

Threshold Lowering and Stable DNA Capture

The FIB milling process affords considerable flexibility in the shapeand dimension of funnels 20 that can be used to interface themicrofluidic and nanofluidic components on a device 10. It iscontemplated that funnel geometries can be selected to minimize theapplied forces, making low velocity transport possible. This may beaccomplished by calculating the force applied to the DNA molecule in thenanochannel under conditions where the entropic force of the molecule'sgradual confinement in the funnel is balanced by the driving force inthe funnel supplied by the applied voltage, pressure, or gravitationalfield. Additionally, the presence of the two opposing forces may resultin a range of applied voltage, pressure, or centripetal force over whicha DNA molecule can be trapped in the funnel indefinitely if appropriatefunnel geometries are used.

Optimal nanofunnel geometries can be determined by the theoreticalmodeling of DNA molecules subjected to the appropriate entropic anddriving forces. In the following examples, DNA molecules are driven intoand through the nanofunnels and nanochannels using an applied voltage.Similar modeling could be readily performed in which the driving forcewas an applied pressure or centripetal force, for example. FIGS. 10A-10Cillustrate the information obtainable from these theoreticalcalculations. For a given funnel geometry, there is a minimum electricfield strength (E_(min)) that must be applied to force the DNA moleculeinto the nanofunnel 20. Above this field strength and for somenanofunnel geometries, the DNA molecule can be stably trapped in thenanofunnel 20. As the voltage is increased, the average position of themolecule moves towards the nanochannel 30. When the electric fieldstrength exceeds a critical value (E_(c)) the DNA molecule is forced outof the trap and is transported through the nanochannel 30. Theoreticalmodeling can determine the characteristic field strengths (E_(min),E_(c)) that define the stable trapping regime, the average position of atrapped DNA molecule (x_(i), x_(f)), its extended length (x_(f)−x_(i)),and the critical voltage that must be applied to drive transport throughthe nanochannel (E_(c)).

Low fields (E<E_(min)) can momentarily trap DNA molecules but areinsufficient to prevent their diffusive escape out of the nanofunnel 20and away from the nanochannel 30. Intermediate fields (E>E_(min),E<E_(c)) can stably trap the DNA in the nanofunnel 20 with the positionof the DNA molecule (x_(i) and x_(f)) dependent on the magnitude of theelectric field. High fields (E>E_(c)) can transport the DNA into andthrough the nanochannel 30. The values of the field strengths E_(min)and E_(c) are dependent on the shape and size of the nanofunnel and thesize of the DNA molecule. For this reason, a theoretical understandingof DNA behavior in a nanofunnel, according to embodiments of theinvention, can be important for establishing these values a priori.

Different nanofunnel shapes can be configured to be optimal fordifferent functions. For example, one nanofunnel can dramatically reducethe voltage required to drive transport into its associated nanochannel,resulting in low velocity DNA transport. The same nanofunnel may have avery limited range of voltages over which the DNA molecule is stablytrapped. In contrast, a second nanofunnel can be optimized to have alarge range of voltages over which trapping in the nanofunnel is stable.This second nanofunnel may require a higher critical voltage, however,to initiate DNA transport through the nanochannel. FIGS. 11A-Dillustrate some elements of nanofunnel shape that have beeninvestigated. The nanochannel width (w) and depth (d) vary with positionalong the nanofunnel's longitudinal axis (x) by the power law w,d˜x^(α).

In some particular embodiments, Equation 1 can be used to define how thenanofunnel width and depth vary as a function of position along thenanofunnel raised to exponent “α”, again based on the desired nanofunneloperational characteristics. In Equation 1, the width and depth arerepresented by a single variable, “D” (shown in FIG. 11A), which is theeffective diameter of the narrow end of the nanofunnel (equivalent tothe nanochannel cross-section dimensions, y is the width or depth of thenanofunnel at position x along the longitudinal (x) axis (also known asthe symmetry or longitudinal centerline axis). The variable x₀ indicatesthe coordinates of the nanofunnel apex, which is also the intersectionof the narrow end of the nanofunnel with the nanochannel. Equation 1therefore reflects that the nanofunnel is seamlessly interfaced with thenanochannel because the nanofunnel critical dimensions are equivalent tothose of the nanochannel when x=x₀.

$\begin{matrix}{{\frac{y}{D} = \left( \frac{x}{x_{0}} \right)^{\alpha}},{x > x_{0}}} & {{EQUATION}\mspace{14mu} 1}\end{matrix}$

However, it is noted that Equation 1 is provided for example only asthere are other equations of similar form that could be used to stretchor compress the nanofunnel while maintaining the same alpha. Thus, anysuitable power law equation can be used to select dimensions fordifferent desired exponents (α) according to what behavior or moleculeis targeted for analysis, based on the proportional relationship:y˜x^(α). Here “y” is understood to represent either of the dimensionswidth or depth. In some embodiments, the width and depth may be definedby the same function of x, yielding a nanofunnel with an aspect ratio(depth:width) of 1 along its entire length. In other embodiments, thewidth and depth may be defined by different functions of x, yielding ananofunnel with an aspect ratio other than 1 (e.g., 0.1, 0.2, 0.5, 2, 4)along its entire length or an aspect ratio that varies along thenanofunnel's length.

Again, as shown with FIGS. 11G and 11F, the nanofunnel 20 can have ashape defined by a concatenation of functions (y₁, y₂, y₃, . . . ) wherethe width and depth of the nanofunnel are defined by y₁ between axialcoordinates x₀ and x₁, by y₂ between axial coordinates x₁ and x₂, by y₃between axial coordinates x₂ and x₃, and so on. Each segment of thenanofunnel can be seamlessly or discontinuously connected to itsneighboring segments and the narrow end of the nanofunnel can beseamlessly connected to a corresponding aligned nanochannel ormicrochannel. The concatenated nanofunnels can consist of 2 to 10segments in some embodiments or can form long fluidic conduitsconsisting of up to hundreds or thousands of segments in otherembodiments.

As shown in FIG. 11E, the funnel 20 can have a configuration where theexponent α can itself be a function of axial position x. This can createmore complicated funnel shapes. FIG. 11E shows a simple example with anexemplary function where the exponent alpha is a function of x. Byhaving the funnel shape defined using a proportionality, y˜x^(α(x)), avariety of scaling factors and constants can be used to adjust thefunnel dimensions. In this example, y˜x^((0.015x+1)) (i.e.,α(x)=0.015x+1), but other scaling factors and exponent multipliers canbe used with y dimension proportional to the x dimension. Furthermore,as shown in FIGS. 11F and 11G, nanofunnels can be configured as a seriesof segments where the dimensions in each segment are defined by adifferent geometric relationship and where the segments are connectedseamlessly (FIG. 11F) or discontinuously (FIG. 11G). FIG. 11A maps anidealized cylindrical funnel onto a coordinate axis to illustrate thefunctional form, y˜x^(α). Funnels for which α<1 are convex, while thosefor which α>1 are concave. FIG. 11B shows a series of funnel shapeshaving different a exponent values. While the power law function allowsinvestigations over a variety of nanofunnel shapes by varying oneparameter, it should not be construed as the exclusive set of funnelgeometries that can be fabricated or assessed theoretically. FIGS. 11C,11D show how the voltage, V, varies along the length of a nanofunnelwhen α<0.5 (FIG. 11C) and when α>0.5 (FIG. 11D). In these plots, alarger slope in the curve corresponds to a higher electric field at theposition, x. When α<0.5 (FIG. 11C), the voltage increases linearly alongthe entire nanofunnel length and can do so indefinitely. When α>0.5(FIG. 11D), the voltage can reach a maximum value, v_(∞), within thenanofunnel, above which the voltage will not increase. To be clear,there are changes in nanofunnel behavior that occur when alpha<0.5 andwhen alpha>0.5, including the voltage profile within the nanofunnel 20(FIGS. 11C and 11D, bottom plots) and the monomer density profile withinthe nanofunnel (FIGS. 12A and 12B, bottom plots).

The nanofunnel shown in FIG. 11C has an alpha=0.3 value while that shownin FIG. 11D has an alpha=0.7 to illustrate the noted changes inbehavior, not the convex or concave nature of the funnels themselves. Inaddition to an understanding of shape-controlled force fields,theoretical predictions of DNA behavior can consider the properties ofthe DNA molecule, specifically its stiffness and length. FIG. 12 showsone important way in which the properties of DNA can affect theoperational parameters of trapping and critical transport voltages. Dueto the voltage profile in a nanofunnel with α<0.5, the electrostaticforce on the trailing end of the DNA molecule acts like a piston,compressing the leading end of the molecule, pushing it towards thenanochannel entrance, and lowering the critical voltage needed to drivetransport. This compression results in a plateau region in the plot ofmonomer concentration, c, as a function of position in the nanofunnel(FIG. 12A). In a nanofunnel with α>0.5, most of the electrostatic forceis on the leading end of the molecule and there is no piston effect. Inthis case, the monomer concentration does not exhibit a compressedplateau region (FIG. 12B).

The theory that was developed to describe DNA molecular behavior innanofunnels was used to predict trends in a molecule's position, itslength, and the critical electric field required to drive transportthrough the nanochannel. The theoretical predictions are compared tosimulation and experiment results. FIG. 13A compares theory (lines) andsimulation results (markers) describing the position of a DNA molecule'sleading end (x_(i)) as a function of applied voltage (proportional toE₀, the electric field magnitude in the nanochannel). Per standardprotocol in theoretical polymer physics, these values are normalized andplotted as dimensionless variables where b is the characteristic DNAKuhn length, q is the charge on the DNA, D is the geometric average ofthe nanochannel width and depth, k is Boltzmann's constant, and T istemperature. Results are plotted for DNA molecules that are 200(diamonds) and 600 (circles) Kuhn lengths long, or approximately 20 and60 μm, respectively. FIG. 13B shows the position of the DNA molecule'strailing end (x_(f)) as a function of applied voltage. The equilibriumlength of the DNA molecule can be determined by the difference,x_(f)−x_(i). FIG. 14 shows a comparison of theory and simulationsdescribing the dependence of the critical electric field required todrive transport through the nanochannel on the power law exponent, α.The dimensionless variable of the plot ordinate is the critical fieldwith the nanofunnel E_(c) ^(f), normalized by the critical fieldnecessary to drive transport through a nanochannel with no funnel,E_(c).

Experimental investigations were conducted to determine the behavior ofDNA molecules in a nanofunnel. Similar to the theoretical efforts, theparameters that were measured included the voltage range of stabletrapping, the position of a trapped DNA molecule, its equilibriumlength, and the critical electric field at which transport through thenanochannel occurs. Fluorescently stained λ-phage and T4-phage DNAmolecules were electrokinetically driven into a funnel at fieldstrengths greater than E_(min). The position of the molecule within thenanofunnel was monitored, typically for over 30 min, and plotted as afunction of time. This data acquisition protocol was repeated over arange of voltages within the stable trapping regime to determine thedependence of the molecule's position and length on the applied voltage.FIG. 15 are graphs and images from a trapping experiment. DNA moleculeswere trapped in the nanofunnels shown in FIG. 15A, Fluorescence imageswere recorded (FIG. 15B) and reduced to an intensity profile (FIG. 15C)characterizing DNA length and position. FIG. 15D shows a time series ofthese frames highlighting the thermal fluctuations in the molecule'slength and position. FIGS. 16 and 17 are graphs of the voltagedependence of trapping position for two DNA molecules having differentcontour lengths (λ-phage, ˜20 μm long, and T4-phage DNA, ˜70 μm long) inan electrophoresis buffer and in some instances, as indicated,containing 2% by weight of a low molecular weight polymer,polyvinylpyrrolidone (PVP). FIG. 18 is a related graph that illustratesthe relationship between the voltage-dependent properties of DNA lengthand trapping position. These two values are correlated because thegreater confinement experienced by the DNA molecule as it is drivendeeper into the funnel results in greater extension. The variances inthese parameters provide a measure of the trap stability vis-à-visthermal fluctuations. Each data point in FIGS. 16-18 represents theaverage of over 20,000 measurements collected over about 30 minutes.

It is contemplated that the use of properly shaped and sized funnels 20can facilitate macromolecule capture, trapping, and transport throughnanochannels 30 having critical dimensions smaller than the radius ofgyration of the molecule. By lowering the threshold force needed todrive translocation, greater control over molecular transport dynamicsmay be achieved. For channels 30 with nanoscale dimensions in width anddepth, confinement of the macromolecule in both of these dimensions isdisfavored by an entropic energy barrier. Therefore, the optimal funnelgeometry can provide a gradual increase in confinement in bothdimensions. This can be achieved by patterning funnels using FIB millingin which the lateral dimensions and shape of the funnel are controlledby the pattern over which the beam is rastered. The depth of the funnelis controlled by varying the dwell time of the ion beam, milling deeperfeatures at the funnel mouth and gradually shallower features towardsthe intersection of the funnel and nanochannel. The introduction of suchfunnels at the entrance to nanochannels has been predicted theoreticallyand verified experimentally to reduce the voltage that must be appliedto electrokinetically drive double-stranded DNA through long FIB-millednanochannels. Additionally, given appropriate funnel geometries andcapture forces, single molecules can be stably trapped and investigatedfor a desired length of time.

The devices 10 and/or nanofunnels 20 can be configured to analyze a DNAmolecule, a protein, a fluorescently stained molecule, and optionallythe analyte molecule can be been modified in any way to provide orenhance analyzing the molecule in a respective nanochannel 20.

The use of FIB milling to fabricate features with control in all threedimensions provides an ultimate degree of flexibility in funnel design.A macromolecule can be gradually driven through an FIB-milled funneldirectly into a nanochannel, transitioning from an unconfined to ahighly confined state. This gradual transition can result intranslocations occurring at low molecular velocities in which themolecule preferentially enters the nanochannel in an unfolded, extendedstate.

The use of funnels to facilitate the threading of macromolecules intonanochannels lowers the threshold force needed to drive translocationand thus lowers the transport velocity, which is expected to enable moreprecise optical and electrical measurements on single confinedmolecules, One example is the sequencing of DNA molecules in ananochannel interfaced to opposed tunneling probes in which base callingis achieved by measuring the unique tunneling currents through theindividual nucleotides. Such a funnel could also be used in isolation(without interfacing it to a long nanochannel) as a conduit between twomicrochannels and serving as a stochastic sensor. Translocations throughthe funnel could be monitored optically (e.g. fluorescently stainedmolecules) and/or electrically (e.g., axial ionic current). A potentialadvantage to this geometry is the seamless integration of microfluidicand nanofluidic components on a single layer device, in contrast tostacked devices that integrate microfluidic channels and nanoporousmembranes. Funnels 20 in which both the width and depth vary graduallyare also believed to be suitable, potentially ideal, platforms uponwhich to study the physical properties of flexible or deformablemacromolecules. Because the FIB milled nanochannels and nanofunnels areeasily interfaced with other fluidic components on a single chip theiruse can be integrated with other technologies such as flow injection,separations in microfluidic channels, and single cell lysis.

The described nanofabrication methodology and devices have applicationto microelectronics and nanofluidics technology. Nanofluidicimplementations with nanochannels of these critical dimensions andquality are well suited for a number of applications including singlemolecule detection and identification, confinement and manipulation ofbiopolymers, biological assays, restriction mapping of polynucleotides,DNA sizing, physical methods of genomic sequencing, and fundamentalstudies of the physics of confinement.

FIG. 19 is a schematic illustration showing experimental evaluations oftranslocation event frequency for DNA molecules electrokineticallydriven through the nanochannel from either the funnel side (right toleft in FIG. 19) or the channel side (left to right in FIG. 19). FIG. 20shows the experimental results of the two experiments shown in FIG. 19.The linear increase of translocation event frequency with appliedvoltage at higher voltages indicates that voltages in this range exceedthe entropic barrier value. In the case of translocations originatingfrom the channel side, the exponential region of the data seen at lowvoltages indicates the presence of an entropic barrier. This barrier isnot observed in translocations originating from the funnel side. FIG. 21is a fluorescence microscopy image that shows further evidence for theexistence of an energy barrier to translocation from the channel side.By applying a voltage (0.5 V) below the threshold for an extended period(1.5 hours), DNA molecules were electrophoretically driven to thenanochannel entrance but the force on the molecules was insufficient todrive translocation. This condition results in DNA concentration at thenanochannel side. The critical electric fields, E_(c), to drive DNAtransport into and through the nanochannels for different nanofunnelgeometries and DNA samples are presented in the table below. All of thenanofunnels have the same length and have a width×depth that increasesfrom about 100 nm×about 100 nm at the nanochannel end (equivalent to thenanochannel width×depth) to about 1.5 μm×about 1.5 μm at the nanofunnelentrance that is interfaced to the microchannel. The nanofunnels differin the exponent, α, that defines their shape.

TABLE 1 ELECTRIC FIELD REQUIRED TO DRIVE DNA INTO NANOCHANNEL CRITICALELECTRIC FIELD FOR EACH DNA SAMPLE (V/cm) λ-PHAGE T4-PHAGE CIRCULARNANOFUNNEL (~20 μm (~70 μm CHAROMID DNA SHAPE length) length) (~18 μmcircumference) α = 0 65 ± 7 65 ± 7 65 ± 7 α = 0.5 16.1 ± 0.7 17.5 ± 0.721.7 ± 0.7 α = 1 10.8 ± 0.7 10.8 ± 0.7 12.3 ± 0.7

In order to compare different funnel geometries in these experiments,and to compare experimental results to theoretical predictions, theelectric field in the funnels and nanochannels can be compared. Todetermine these fields, the nanochannel and nanofunnel shape (width anddepth) can be precisely determined using atomic force microscopy (FIGS.22A, 22B), SEM imaging (FIGS. 3B, 3C, 7A, 7B, 7C, 23), and ion beamtomography, for example. The optimal shape(s) may change formacromolecules having different physical properties, systems withdifferent polymer-solvent intermolecular interactions, and drivingforces with different flow profiles, all parameters that can beinvestigated theoretically.

FIG. 23 illustrates a bitmap image 20 bm used to create a correspondingFIB milled funnel 20 and nanochannel 30 (SEM image) with a length ofabout 22 μm and a graph of an AFM (Atomic Force microscopy) image ofwidth (μm) versus length (μm).

FIG. 24 is a graph showing a parabolic relationship of depth and widthover a length of the nanofunnel 20 according to some embodiments of thepresent invention. That is, the nanofunnel(s) 20 can be configured tohave both width and depth dimensions that vary in a parabolic, linearmanner over its length according to some embodiments of the presentinvention.

FIG. 25 shows AFM images of nanofunnels defined by a power law functionwith a values of 0, 0.5, and 1. Devices incorporating such nanofunnelswere used to determine the results represented in the table above. Thegray or color scale labeled “Depth (μm)” on the right hand side of thefigure shows how the intensities of the nanofunnel profiles on the lefthand side of the figure correspond to nanofunnel depth.

Because these characterizations of nanofunnel dimensions provide anaccurate determination of electric field strengths through thenanochannel/nanofunnel conduit, direct comparisons between experimentalresults and theoretical predictions can be made. FIG. 26A illustratesthe comparison between the experimentally determined positions of theleading and tailing ends of a trapped λ-phage DNA molecule. FIG. 26Billustrates the comparison between the experimentally determinedpositions of the leading and tailing ends of a trapped T4-phage DNAmolecule. FIG. 27 is a schematic illustration of an analysis system 100which includes at least one device 10 with at least one nanofunnel 20,electrodes 70 and a control circuit 101 with a funnel applied voltagemode and a channel applied voltage mode, the funnel mode configured toapply a larger voltage than the channel mode.

FIG. 28 is a schematic illustration of a fabrication system 201 with amilling apparatus 200 and a circuit 200 c with a nanofunnel patterningfile 200 f which can be totally onboard the apparatus 200, partiallyonboard the apparatus 200 or remote from the apparatus such as in one ormore servers 225.

The foregoing is illustrative of the present invention and is not to beconstrued as limiting thereof. Although a few exemplary embodiments ofthis invention have been described, those skilled in the art willreadily appreciate that many modifications are possible in the exemplaryembodiments without materially departing from the novel teachings andadvantages of this invention. Accordingly, all such modifications areintended to be included within the scope of this invention as defined inthe claims. The invention is defined by the following claims, withequivalents of the claims to be included therein.

That which is claimed:
 1. A method of forming a chip with fluidicchannels, comprising: forming at least one nanofunnel with a wide endand a narrow end into a planar substrate, wherein the at least onenanofunnel has a length, with width and depth dimensions that both varyover the length, wherein the forming the at least one nanofunnel iscarried out using milling directed by an electronic patterning file on acomputer configured to direct a milling to have a defined dwell time atdefined X and Y coordinates to generate the nanofunnel width and depthdimensions over its length, and wherein an X axis is collinear with thenanofunnel length and a Y axis is collinear with the nanofunnel width;forming at least one nanochannel or microchannel into the planarsubstrate at an interface adjacent the narrow end of the at least onenanofunnel and with the wide end of the at least one nanofunnelproximate a microchannel used for fluidic sample introduction into thenanofunnel, wherein the microchannel for fluidic sample introduction issized and configured so that sample molecules are unconfined within themicrochannel residing proximate the wide end of the at least onenanofunnel, wherein the at least one nanochannel or microchannel has alength, with width and depth dimensions; and sealing a flat cover to thesubstrate directly over an open upper surface of the nanofunnel and anopen upper surface of the nanochannel or the microchannel to define afluidic chip; wherein the length of the at least one nanofunnel and thelength of the at least one nanochannel or microchannel both extend alonga plane of a primary surface of the planar substrate and the depthdimension of the at least one nanofunnel and the at least onenanochannel or microchannel extend in a direction that is into the planeof the primary surface of the substrate, and wherein the fluidic chipcomprising the at least one nanofunnel and the at least one nanochannelor microchannel is adapted to analyze a molecule of DNA, proteins orother polymeric material as the sample molecules.
 2. The method of claim1, wherein both of the forming steps are carried out using focused ionbeam (FIB) milling.
 3. The method of claim 1, wherein the forming the atleast one nanofunnel and the forming a corresponding aligned one of theat least one nanochannel or microchannel are both carried out during asingle milling operation using a Focused Ion Beam (FIB) milling devicethat transmits an FIB beam into the substrate and the electronicpattering file on a computer that controls a dwell time of the FIB beamat X and Y coordinates to seamlessly connect the nanochannel ormicrochannel to the narrow end of the nanofunnel.
 4. The method of claim1, wherein the at least one nanofunnel width and depth dimension vary ina user-defined geometric relationship over substantially an entirelength of a respective nanofunnel to alter a cross-sectional size of therespective nanofunnel by at least a factor of two from the wide end tothe narrow end.
 5. The method of claim 1, wherein the at least onenanofunnel is comprised of a concatenated series of portions in which arespective width and depth dimension vary in a user-defined geometricrelationship over an entire length of each portion, wherein the widthand depth of each portion is defined by a different geometric function,and wherein neighboring portions are seamlessly or discontinuouslyconnected.
 6. The method of claim 1, wherein the at least one nanofunnelcomprises at least a portion with a substantially parabolic contour. 7.The method of claim 1, wherein the at least one nanofunnel comprises atleast a portion with a substantially convex contour.
 8. The method ofclaim 1, wherein the at least one nanofunnel comprises at least aportion with a substantially concave contour.
 9. The method of claim 1,wherein the at least one nanofunnel has walls that angle inward at aconstant slope.
 10. The method of claim 1, wherein the formed at leastone nanochannel or microchannel includes a nanochannel that is alignedwith and downstream of the narrow end of a respective nanofunnel of theat least one nanofunnel, wherein the aligned nanochannel hassubstantially constant width and depth dimensions, and wherein thenarrow end of the respective nanofunnel has width and depth dimensionsthat substantially match a respective width and depth dimension of thealigned nanochannel.
 11. The method of claim 1, wherein the forming theat least one nanofunnel is carried out to generate a nanofunnel withwidth and depth dimensions that both vary over the length of thenanofunnel according to a power law (width˜X^(α) and depth˜X^(α)), whereX is the coordinate along the nanofunnel length and alpha (“α”) is apositive number.
 12. The method of claim 11, wherein the positive numberfor a is configured as a function of the coordinate along the nanofunnellength X where α=f(X)>0 for all X.
 13. The method of claim 1, whereinthe at least one nanofunnel is a plurality of nanofunnels and each has alength that is between 1 um to 100 um.
 14. The method of claim 1,wherein the forming steps are carried out to place the wide end of theat least one nanofunnel proximate the microchannel for the fluidicsample introduction and to place the narrow end of a correspondingnanofunnel of the at least one nanofunnel as a funnel shaped entrance toan aligned nanochannel of the at least one nanochannel or microchannelas the interface, and wherein the aligned nanochannel has an aspectratio (AR) of depth:width that is about 10 or less.
 15. The method ofclaim 1, wherein the at least one nanofunnel has opposing sidewalls thatface each other across the width dimension and extend into the substratein a direction of the depth dimension, and wherein the at least onenanofunnel has an open upper surface and a closed bottom surface betweenthe sidewalls.
 16. The method of claim 1, wherein the substrate is amolded substrate.
 17. The method of claim 16, wherein the substratecomprises an elastomer and/or polymer or plastic.